Band Diagram of Spin Waves in a Two-Dimensional Magnonic Crystal

The dispersion curves of collective spin-wave excitations in a magnonic crystal consisting of a square array of interacting saturated nanodisks have been measured by Brillouin light scattering along the four principal directions of the first Brillouin zone. The experimental data are successfully compared to calculations of the band diagram and of the Brillouin light scattering cross section, performed through the dynamical matrix method extended to include the dipolar interaction between the disks.We found that the fourfold symmetry of the geometrical lattice is reduced by the application of the external field and therefore equivalent directions of the first Brillouin zone are characterized by different dispersion relations of collective spin waves. The dispersion relations are explained through the introduction of a bidimensional effective wave vector that characterizes each mode in this magnonic metamaterial.